The Bible says to love your enemies, but it also teaches an eye for an eye. Isn’t this a contradiction?

   God is a God of love and He never teaches us to hate, seek revenge, or pay somebody back for wrong doing!  Regarding these passages (Matthew 5:38-43) you must read them very closely.  In fact, Jesus is not quoting the O.T. here, but the Pharisaical misinterpretation of the Old Testament.  Notice that Jesus did not say, "It is written," as He often did when quoting the Old Testament.  Rather He said "you have heard", or "it has been said" by which he meant the Jewish "tradition" that had grown up around the Old Testament. The Jews took their traditions and made the Commandment of God of no effect (Matthew 15:3, 6).  The truth is that a God of love commanded us to love in the Old Testament and New Testament. He never said to hate or get revenge of any type.